First find the absolute deviation for each coordinate.
(1,3), (6,2.5), (0.5,8), (4,1), (7.5,1.5), (12,9), (10,13), (11,4).
I will do the 1st coordinate: (1,3)
Least absolute deviation line equation: m(x)= 0.1 x + 2.9
If you plot all 8 coordinates onto a xy graph, m(x) is the line of best fit.
The distance from one coordinate's y-value from the line m(x) is the deviation.
Plug in x from coordinate (1,3) into the equation m(1):
At x = 1, m(1)= 0.1(1) + 2.9 = 3.0
This is (1,3) on the m(x) line.
Find the distance of coordinate (1,3) from (1,3):
Absolute Deviation = |m(1) - y| = |3 - 3| = 0
Repeat for 2nd coordinate: (6, 2.5)
m(6) = 0.1(6) + 2.9 = 3.5
(6,3.5) on the m(x) line.
Absolute Deviation: |m(6) - y| = |3.5 - 2.5| = 1.0
Repeat this again for the other six coordinates.
Add up the eight absolute deviations to find the sum.
The least absolute deviation line equation for the data in the table is m = 0.1 x + 2.9
X 1,6,0.5,4,7.5,12,10,11 y 3,2.5,8,1,1.5,9,13,4
What is the sum of the absolute deviations?
1 answer
1 answer